Geometric moment invariants

Abstract

This paper derives moment invariants in an intuitive way by multiple
integrals of invariant geometric primitives like distance, area and
volume. Many existing 2-D and 3-D moment invariants are re-expressed
to prove the correctness of this method. Furthermore, this construction
method can be easily extended to higher dimensional space and get
higher-order moment invariants. Explicit expressions of 3-D moment
invariants are generated automatically with the help of symbolic
computation software and can be regarded as a kind of shape descriptor
for the representation of solid objects.